Math Gr 9 Nov Exam (Medium)

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What is the commutative property of addition?

a + b = b + a (correct)

a × b = a - b

a × b = a + b

a + b = a - b

Which of the following properties is not applicable to subtraction and division?

Multiplicative property of 1

Commutative property (correct)

Associative property

Distributive property

What is the associative property of multiplication?

(a × b) × c = a × (b × c) (correct)

(a × b) × c = a × (b + c)

(a + b) × c = a + (b × c)

(a × b) × c = a × (c × b)

What is the additive property of 0?

a + 0 = a Signup and view all the answers

What is the purpose of using the distributive property of multiplication over addition?

To break down complex multiplications into simpler parts Signup and view all the answers

How can the commutative and associative properties help in simplifying calculations?

By changing the order of numbers being added or multiplied Signup and view all the answers

What is the purpose of estimating in calculations with whole numbers?

To get close to an exact answer without doing precise calculations Signup and view all the answers

What is the purpose of a summary table for multiplication?

To practice and reinforce the multiplication of various numbers Signup and view all the answers

What is the definition of a multiple of a number?

The product of a number and an integer. Signup and view all the answers

What is the definition of a prime number?

A natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Signup and view all the answers

What is the purpose of finding the least common multiple (LCM)?

To find a common denominator for adding fractions. Signup and view all the answers

What is the process of expressing a number as the product of its prime factors?

Prime factorization Signup and view all the answers

What is the definition of a composite number?

A natural number greater than 1 that can be formed by multiplying two smaller natural numbers. Signup and view all the answers

What is the formula for calculating distance?

Distance = Speed × Time Signup and view all the answers

What is the purpose of finding the highest common factor (HCF)?

To simplify fractions to their lowest terms. Signup and view all the answers

How do you find the time required to process a certain amount based on a rate?

Divide the total amount by the rate. Signup and view all the answers

What is the definition of a rate?

Describes how one quantity changes in relation to another. Signup and view all the answers

What is the purpose of expressing a ratio?

To identify the relationship between quantities in patterns. Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

What is the effect of subtracting a positive integer from a number?

It decreases the value Signup and view all the answers

What is the product of a positive integer and a negative integer?

Negative Signup and view all the answers

What property of integers allows flexibility in computation and simplification?

All of the above Signup and view all the answers

What is the purpose of rounding off numbers in calculations?

To simplify calculations and make quick decisions Signup and view all the answers

What is the result of adding a negative integer to a number?

It decreases the value Signup and view all the answers

What is the method of breaking down numbers into parts and adding each part separately?

Expanded Notation Signup and view all the answers

What is the symbol used to indicate 'greater than' in comparing integers?

> Signup and view all the answers

What is the result of multiplying a positive integer and a positive integer?

Positive Signup and view all the answers

What is the technique of rearranging parts to make subtraction easier by borrowing from higher place values?

Borrowing Technique Signup and view all the answers

What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?

Multiplication in Parts Signup and view all the answers

What is the result of dividing a positive integer by a negative integer?

Negative Signup and view all the answers

What is the purpose of compensating in calculations?

To adjust for errors introduced by rounding Signup and view all the answers

What is the purpose of the Distributive Property of integers?

To multiply integers over addition and subtraction Signup and view all the answers

What is the result of subtracting a negative integer from a number?

It increases the value Signup and view all the answers

What is the method of aligning numbers vertically by their place values and adding each column?

Column Addition Signup and view all the answers

What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?

Long Division Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the method of subtracting numbers by aligning them by their place values and subtracting each column?

Column Subtraction Signup and view all the answers

What is the purpose of carrying over in multiplication?

To write down the partial product and carry over extra values to the next column Signup and view all the answers

What is the property of addition that states that changing the order of the numbers does not change the sum?

Commutative Property Signup and view all the answers

What is the property of multiplication that states that changing the grouping of the numbers does not change the product?

Associative Property Signup and view all the answers

What is the formula to calculate simple interest?

Interest = Principal × Rate × Time Signup and view all the answers

What is the property of multiplication that states that multiplication distributes over addition?

Distributive Property Signup and view all the answers

What is the result of subtracting a positive integer from another positive integer?

The result can be either positive or negative Signup and view all the answers

What is the additive inverse of an integer?

The negative counterpart of the number Signup and view all the answers

What is the result of adding two positive integers?

A positive sum Signup and view all the answers

What is the process of dividing quantities in a ratio?

Sum the parts of the ratio, divide the total quantity by the sum of the parts, and multiply by the number of parts each entity should receive. Signup and view all the answers

What is the marked price of an article if the selling price is $120 and the discount is 20%?

$150 Signup and view all the answers

What is the result of subtracting a larger integer from a smaller one?

A negative difference Signup and view all the answers

What is the result of multiplying two integers with the same sign?

A positive product Signup and view all the answers

What is the absolute value of -5?

5 Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

The result is always negative Signup and view all the answers

What is the formula for equivalent fractions?

$\frac{a \times k}{b \times k} = \frac{a}{b}$ Signup and view all the answers

What is the formula to calculate profit percentage?

Profit percentage = (Selling price - Cost price) / Cost price × 100 Signup and view all the answers

What is the purpose of finding equivalent fractions?

To compare fractions Signup and view all the answers

What is the result of adding a positive integer and a negative integer?

The result can be either positive or negative Signup and view all the answers

What is the result of multiplying a fraction by a non-zero number?

The value of the fraction remains unchanged Signup and view all the answers

What is the cube of -2?

-8 Signup and view all the answers

What is the process of scaling quantities in a recipe?

Use the ratio of ingredients to the number of servings to scale up or down as needed. Signup and view all the answers

What is the first step in multiplying decimal fractions?

Convert the decimals to whole numbers by multiplying by powers of 10 Signup and view all the answers

When dividing a total amount by a certain number of people, what is the first step?

Convert the total amount to a decimal if necessary Signup and view all the answers

What is the purpose of the additive inverse in integer operations?

To find the sum of an integer and its negative counterpart Signup and view all the answers

What is the result of adding an integer and its additive inverse?

Zero Signup and view all the answers

What is the purpose of the commutative property of multiplication?

To ensure that the product of multiplication is always the same regardless of the order of the factors Signup and view all the answers

What is the result of subtracting an integer from itself?

Zero Signup and view all the answers

What is the purpose of converting the divisor to a whole number in division of decimal fractions?

To ensure that the divisor is a whole number Signup and view all the answers

What is the result of adding an integer and its negative counterpart?

Zero Signup and view all the answers

What is the purpose of adjusting the decimal point in the result of multiplication of decimal fractions?

To ensure that the decimal point is in the correct position Signup and view all the answers

What is the purpose of using the associative property of addition in decimal operations?

To ensure that the order of addition does not change the result Signup and view all the answers

What property of integers allows for flexibility in computation and simplification?

Distributive Property Signup and view all the answers

What is the result of raising a number to the power of zero?

1 Signup and view all the answers

What is the first step in adding or subtracting fractions?

Find the least common multiple of the denominators Signup and view all the answers

What is the product of a negative integer and a negative integer?

Positive Signup and view all the answers

How do you multiply fractions?

Multiply the numerators and denominators together Signup and view all the answers

What is the purpose of expressing large numbers in scientific notation?

To make numbers easier to read Signup and view all the answers

What is the reciprocal of a fraction?

The same fraction with the numerator and denominator swapped Signup and view all the answers

What is the result of cubing a fraction?

A new fraction where both the numerator and the denominator are cubed Signup and view all the answers

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common divisor Signup and view all the answers

What is the result of multiplying a fraction by its reciprocal?

1 Signup and view all the answers

What is the Power of a Product rule?

(ab)^m = a^m × b^m Signup and view all the answers

How do you convert a fraction to a decimal?

Divide the numerator by the denominator Signup and view all the answers

What is the result of multiplying a positive integer and a positive integer?

Positive Signup and view all the answers

What is the purpose of combining integers using the order of operations (PEMDAS/BODMAS)?

To simplify expressions Signup and view all the answers

What is the purpose of finding the least common multiple of the denominators?

To add or subtract fractions with different denominators Signup and view all the answers

What is the result of dividing a fraction by 1?

The original fraction Signup and view all the answers

What is the result of subtracting a negative integer from a number?

Increases the value Signup and view all the answers

What is the purpose of equivalent fractions?

To represent the same value in different forms Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

No change in the value Signup and view all the answers

How do you convert a fraction to a percentage?

Multiply the fraction by 100 Signup and view all the answers

In the sequence of square numbers, what is the formula for the nth term?

T_n = n^2 Signup and view all the answers

What is the relationship between the number of calls made and the airtime left on a cell phone?

Direct influence, as the number of calls affects the airtime left. Signup and view all the answers

What is the formula for the nth term of triangular numbers?

T_n = n(n + 1)/2 Signup and view all the answers

What type of pattern does the formula T_n = T_1 + (n - 1) * d represent?

Arithmetic progression Signup and view all the answers

What is the term for different expressions that represent the same value or relationship?

Equivalent forms Signup and view all the answers

What is the purpose of a flow diagram?

All of the above Signup and view all the answers

What type of relationship exists between the number of learners at a school and the number of classrooms needed?

Direct influence Signup and view all the answers

What is the term for a variable quantity that is influenced by another variable quantity?

Influenced quantity Signup and view all the answers

What is the formula for the nth term of a geometric progression?

T_n = T_1 * r^(n-1) Signup and view all the answers

What is the formula for dividing a fraction by another fraction?

( \frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} × \frac{d}{c} ) Signup and view all the answers

What is the formula for simplifying a fraction?

( \frac{a}{b} = \frac{a ÷ GCD(a, b)}{b ÷ GCD(a, b)} ) Signup and view all the answers

What is the relationship between the number of matches in an arrangement and the number of triangles in the arrangement?

Direct influence, as more matches create more triangles Signup and view all the answers

What is the formula for converting a fraction to a percentage?

( \text{Percentage} = \frac{a}{b} × 100 ) Signup and view all the answers

What is the formula for finding the percentage of a given number?

( \text{Percentage of a number} = \frac{\text{Percentage}}{100} × \text{Number} ) Signup and view all the answers

What is the formula for increasing a number by a percentage?

( \text{Increased Value} = \text{Original Number} + \frac{\text{Percentage}}{100} × \text{Original Number} ) Signup and view all the answers

What is the result of adding a negative integer to its additive inverse?

Zero Signup and view all the answers

What is the formula for decreasing a number by a percentage?

( \text{Decreased Value} = \text{Original Number} - \frac{\text{Percentage}}{100} × \text{Original Number} ) Signup and view all the answers

What is the formula for calculating the percentage change?

( \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} × 100 ) Signup and view all the answers

What property of multiplication states that the order of the factors does not change the product?

Commutative Property Signup and view all the answers

What is the formula for converting a percentage to a fraction?

( \text{Fraction} = \frac{\text{Percentage}}{100} ) Signup and view all the answers

What is the formula for the nth term of a sequence with a constant difference?

Tn = T1 + (n - 1) × d Signup and view all the answers

What is the formula for finding a fraction of a fraction?

( \frac{a}{b} × \frac{c}{d} = \frac{a × c}{b × d} ) Signup and view all the answers

What is the purpose of using the additive inverses in integer operations?

To simplify calculations Signup and view all the answers

What is the formula for adding decimal fractions?

Align the decimal points and add the numbers. Signup and view all the answers

What is the relationship between adding a positive integer and subtracting its additive inverse?

They have the same effect Signup and view all the answers

What is the formula for the nth term of a sequence with a constant ratio?

Tn = T1 × r^(n-1) Signup and view all the answers

What is the result of subtracting a negative integer from a number?

An increase in the value Signup and view all the answers

What is the purpose of using the distributive property of multiplication?

To simplify calculations involving multiplication and addition Signup and view all the answers

What is the symbol used to indicate 'greater than' in comparing integers?

> Signup and view all the answers

What is the formula for the nth term of a sequence following a linear pattern?

Tn = a × n + b Signup and view all the answers

What is the process of finding an equivalent fraction in its simplest form?

Dividing the numerator and the denominator by their greatest common divisor (GCD) Signup and view all the answers

Which of the following is an example of an equivalent decimal?

0.5 and 1/2 Signup and view all the answers

What is the purpose of combining like terms in algebraic expressions?

To simplify the expression Signup and view all the answers

How can you convert a decimal to a fraction?

Write the decimal as a fraction with a denominator of a power of 10 and then simplify Signup and view all the answers

What is the distributive property of multiplication over addition?

a(b + c) = ab + ac Signup and view all the answers

What is the purpose of using flow diagrams in algebra?

To represent the sequence of operations visually Signup and view all the answers

What is the result of simplifying the expression 2(x + 3)?

2x + 6 Signup and view all the answers

What is the purpose of factoring algebraic expressions?

To express algebraic expressions as a product of their factors Signup and view all the answers

What is the result of combining like terms in the expression 2x + 3x?

5x Signup and view all the answers

What is the purpose of using the order of operations in algebra?

To follow a specific order when performing calculations Signup and view all the answers

What is the purpose of the commutative property of addition?

To allow flexibility in adding numbers in any order Signup and view all the answers

Which property allows us to multiply numbers in any order?

Commutative property Signup and view all the answers

What is the purpose of the associative property of addition?

To allow flexibility in adding numbers when more than two numbers are involved Signup and view all the answers

What is the purpose of using the distributive property of multiplication over addition?

To break down complex multiplication into simpler parts Signup and view all the answers

What is the purpose of a summary table for multiplication?

To practice and reinforce the multiplication of various numbers Signup and view all the answers

What is the purpose of estimating in calculations with whole numbers?

To get close to the answer without doing precise calculations Signup and view all the answers

What is the additive property of 0?

a + 0 = a Signup and view all the answers

What is the multiplicative property of 1?

a x 1 = a Signup and view all the answers

What is the purpose of estimating products by rounding to the nearest thousand?

To simplify the calculation and get a quick approximation Signup and view all the answers

What is the benefit of using the column addition method?

It helps to simplify the calculation by aligning numbers by their place values Signup and view all the answers

What is the method of subtracting numbers by aligning them by their place values and subtracting each column?

Column subtraction Signup and view all the answers

What is the purpose of compensating in calculations?

To correct for errors introduced by rounding Signup and view all the answers

What is the method of breaking down numbers into parts and adding each part separately?

Expanded notation Signup and view all the answers

What is the purpose of using the borrowing technique in subtraction?

To simplify the calculation by rearranging parts Signup and view all the answers

What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?

Multiplication in parts Signup and view all the answers

What is the main difference between a prime number and a composite number?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, while a composite number can be formed by multiplying two smaller natural numbers. Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?

Long division Signup and view all the answers

What is the purpose of finding the least common multiple (LCM) of two or more numbers?

To find a common denominator for adding fractions. Signup and view all the answers

What is the process of expressing a number as the product of its prime factors called?

Prime factorization. Signup and view all the answers

What is the purpose of carrying over in multiplication?

To write down the partial product and carry over extra values to the next column Signup and view all the answers

How do you determine if a number is prime?

Check if the number can be divided evenly by any prime numbers smaller than its square root. Signup and view all the answers

A recipe for 4 servings requires 2 cups of flour. How many cups of flour are needed for 8 servings?

4 cups Signup and view all the answers

What is the formula to calculate distance when given the speed and time?

Distance = Speed × Time. Signup and view all the answers

A bicycle travels 60 km in 2 hours. What is its speed?

60 km/h Signup and view all the answers

What is the selling price of an article marked at $150 with a 15% discount?

$127.50 Signup and view all the answers

What is the purpose of expressing a ratio?

To compare two quantities. Signup and view all the answers

What is the result of multiplying (-3) by 4?

-12 Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

Always negative. Signup and view all the answers

What is the purpose of finding the highest common factor (HCF) of two or more numbers?

To simplify fractions to their lowest terms. Signup and view all the answers

What is the absolute value of (-8)?

8 Signup and view all the answers

What is the result of adding 5 and (-3)?

2 Signup and view all the answers

What is the method of dividing quantities in a ratio called?

Ratios and proportions. Signup and view all the answers

What is the result of dividing $120 by a ratio of 3:4?

$72 Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder. Signup and view all the answers

What is the profit percentage if the selling price is $120 and the cost price is $100?

20% Signup and view all the answers

What is the cube of (-2)?

-8 Signup and view all the answers

What is the result of subtracting (-3) from 5?

8 Signup and view all the answers

What is the result of adding an integer to its additive inverse?

The result is zero. Signup and view all the answers

What is the effect of subtracting a negative integer from a number?

The result is increased by the value. Signup and view all the answers

What is the product of two negative integers?

The product is always positive. Signup and view all the answers

What is the purpose of the distributive property of multiplication?

To simplify calculations involving multiple operations. Signup and view all the answers

What is the result of adding two negative integers?

The result is always negative. Signup and view all the answers

What is the purpose of the commutative property of addition?

To allow flexibility in the order of operations in addition. Signup and view all the answers

What is the result of multiplying a negative integer by a positive integer?

The result is always negative. Signup and view all the answers

What is the purpose of the associative property of addition?

To allow flexibility in the order of operations in addition. Signup and view all the answers

What is the result of subtracting a positive integer from another positive integer?

The result depends on the values of the integers. Signup and view all the answers

What is the result of multiplying two positive integers?

The result is always positive. Signup and view all the answers

What is the purpose of the associative property of addition?

To ensure that the sum of the numbers remains the same when the grouping of the numbers is changed Signup and view all the answers

What is the formula to find an equivalent fraction?

$\frac{a}{b} = \frac{a \times k}{b \times k}$ Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

A negative integer Signup and view all the answers

What is the purpose of the additive inverse of an integer?

To find the sum of a number and its negative counterpart Signup and view all the answers

What is the result of adding a positive integer and its additive inverse?

Zero Signup and view all the answers

What is the property of multiplication that states that the product of two numbers remains the same even if the order of the numbers is changed?

Commutative property of multiplication Signup and view all the answers

What is the distributive property of multiplication?

Multiplication distributes over addition and subtraction Signup and view all the answers

What is the result of subtracting a positive integer from a negative integer?

A negative integer Signup and view all the answers

What is the identity property of multiplication?

Multiplying a number by one results in the number Signup and view all the answers

What is the absolute value of an integer?

The distance between the number and zero on the number line Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

Negative Signup and view all the answers

Which of the following properties is true about multiplication?

All of the above Signup and view all the answers

What is the result of raising a number to the power of zero?

One Signup and view all the answers

What is the purpose of using exponential form?

To simplify calculations Signup and view all the answers

What is the result of cubing a fraction?

A new fraction where both the numerator and the denominator are cubed Signup and view all the answers

What is the purpose of using scientific notation?

To simplify calculations involving large or small numbers Signup and view all the answers

What is the result of dividing a positive integer by a negative integer?

Negative Signup and view all the answers

What is the purpose of the power of a product rule?

To simplify calculations involving multiplication Signup and view all the answers

What is the result of squaring a fraction?

A new fraction where both the numerator and the denominator are squared Signup and view all the answers

What is the purpose of the quotient of powers rule?

To simplify calculations involving division Signup and view all the answers

What is the first step in adding or subtracting fractions?

Find the least common multiple of the denominators Signup and view all the answers

What is the formula for multiplying fractions?

( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} ) Signup and view all the answers

What is the purpose of simplifying fractions?

To reduce the fraction to its simplest form Signup and view all the answers

How do you convert a fraction to a decimal?

By dividing the numerator by the denominator Signup and view all the answers

What is the formula for converting a fraction to a percentage?

( \frac{a}{b} \times 100 ) Signup and view all the answers

What is the term for a fraction that represents a part of a whole divided into ten equal parts?

Tenth Signup and view all the answers

What is the formula for dividing fractions?

( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} ) Signup and view all the answers

What is the purpose of equivalent fractions?

To represent the same value Signup and view all the answers

What is the formula for finding a fraction of a fraction?

( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} ) Signup and view all the answers

What is the formula for simplifying a fraction?

( \frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} ) Signup and view all the answers

What is the result of adding a negative integer to its additive inverse?

0 Signup and view all the answers

If $a$ and $b$ are integers, what is the result of $a × (b - c)$?

$a × b - a × c$ Signup and view all the answers

What is the formula to find a fraction of a fraction?

$$ rac{a}{b} \div rac{c}{d} = rac{a}{b} imes rac{c}{d} $$ Signup and view all the answers

What is the purpose of identifying the rule in a sequence of numbers?

To find the next term in the sequence Signup and view all the answers

What is the result of subtracting a negative integer from a number?

An increase in the value Signup and view all the answers

What is the method to simplify a fraction?

Dividing both the numerator and denominator by their greatest common divisor Signup and view all the answers

If $a$ and $b$ are integers, what is the result of $a + (-b)$?

$a - b$ Signup and view all the answers

What is the formula to convert a fraction to a percentage?

$$ ext{Percentage} = rac{a}{b} imes 100 $$ Signup and view all the answers

What is the purpose of using the formula $T_n = T_1 + (n - 1) × d$ in a sequence?

To determine the next term in the sequence Signup and view all the answers

What is the method to find the percentage of a given number?

Converting the percentage to a fraction and then multiplying by the number Signup and view all the answers

What is the result of adding a positive integer to a number?

An increase in the value Signup and view all the answers

What is the formula to increase a number by a percentage?

$$ ext{Increased Value} = ext{Original Number} + \left( rac{ ext{Percentage}}{100} imes ext{Original Number} ight) $$ Signup and view all the answers

What is the purpose of using the formula $T_n = a × n + b$ in a sequence?

To determine the next term in a linear sequence Signup and view all the answers

What is the formula to find the percentage change?

$$ ext{Percentage Change} = \left( rac{ ext{New Value} - ext{Original Value}}{ ext{Original Value}} ight) imes 100 $$ Signup and view all the answers

What is the result of subtracting a positive integer from a number?

A decrease in the value Signup and view all the answers

What is the formula to convert a percentage to a fraction?

$$ ext{Fraction} = rac{ ext{Percentage}}{100} $$ Signup and view all the answers

What is the purpose of using the formula $T_n = T_1 × r^{(n-1)}$ in a sequence?

To determine the next term in a sequence with a constant ratio Signup and view all the answers

What is the method to add decimal fractions?

Aligning the decimal points and adding the numbers Signup and view all the answers

What is the formula to find the decreased value of a number by a percentage?

$$ ext{Decreased Value} = ext{Original Number} - \left( rac{ ext{Percentage}}{100} imes ext{Original Number} ight) $$ Signup and view all the answers

What is the formula to compare quantities using percentages?

$$ ext{Comparison as Percentage} = \left( rac{ ext{Part}}{ ext{Whole}} ight) imes 100 $$ Signup and view all the answers

When adding or subtracting decimal fractions, what is the correct step to follow?

Align the decimal points and then add or subtract corresponding digits. Signup and view all the answers

What is the purpose of converting decimal fractions to whole numbers when multiplying?

To eliminate the decimals and perform the multiplication as with whole numbers Signup and view all the answers

When dividing a decimal fraction by another decimal fraction, what is the correct step to follow?

Convert the divisor to a whole number by multiplying both numbers by a power of 10, then divide Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

Which property of multiplication allows flexibility in computation and simplification?

Associative Property Signup and view all the answers

What is the purpose of using the additive inverse in calculations?

To simplify calculations by adding opposite numbers Signup and view all the answers

When comparing integers, what symbol is used to indicate 'greater than'?

> Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

A negative integer Signup and view all the answers

What is the purpose of using the commutative property of addition?

To simplify calculations by changing the order of the numbers Signup and view all the answers

What is the result of subtracting a negative integer from a number?

A positive integer Signup and view all the answers

What is the purpose of finding the greatest common divisor (GCD) in simplifying fractions?

To find an equivalent fraction in its simplest form Signup and view all the answers

What is the result of applying the distributive property to the expression 2(x + 3)?

2x + 6 Signup and view all the answers

What is the purpose of converting a fraction to a decimal?

To perform calculations with fractions Signup and view all the answers

What is the result of combining like terms in the expression 2x + 3x?

5x Signup and view all the answers

What is the purpose of using the distributive property in algebraic expressions?

To multiply a single term by each term within a parenthesis Signup and view all the answers

What is the result of expanding the expression 2(x - 3)?

2x - 6 Signup and view all the answers

What is the purpose of simplifying algebraic expressions?

To make calculations easier Signup and view all the answers

What is the result of converting the decimal 0.5 to a fraction?

1/2 Signup and view all the answers

What is the purpose of using factoring in algebraic expressions?

To express an algebraic expression as a product of its factors Signup and view all the answers

What is the result of simplifying the algebraic expression 2x + 4x?

6x Signup and view all the answers

What is the formula for the nth triangular number?

Tn = n(n + 1)/2 Signup and view all the answers

What type of pattern is represented by the formula Tn = T1 + (n - 1) ⋅ d?

Arithmetic progression Signup and view all the answers

What is the relationship between the number of calls made and the airtime left on a cell phone?

The more calls you make, the less airtime you have left. Signup and view all the answers

What is the phrase used to describe different expressions that represent the same value or relationship?

Equivalent forms Signup and view all the answers

What is the purpose of a flow diagram?

To show the calculations needed to produce output numbers from input numbers. Signup and view all the answers

What type of quantities are age and the number of fingers on your hands?

Age is variable, and the number of fingers is constant. Signup and view all the answers

What is the relationship between the number of identical houses to be built and the number of bricks required?

More houses require more bricks. Signup and view all the answers

What is the purpose of identifying relationships between variables?

To find a specific value of one quantity linked to a value of the other quantity. Signup and view all the answers

What type of diagram shows the calculations needed to produce output numbers from input numbers?

Flow diagram Signup and view all the answers

What is the purpose of describing the relationship between input and output numbers?

To illustrate the calculation process and the connection between input and output numbers. Signup and view all the answers

What is the result of adding 0 to a whole number?

The result is always equal to the original number Signup and view all the answers

Which property allows us to regroup numbers when adding or multiplying three or more numbers?

Associative Property Signup and view all the answers

What is the purpose of using the Distributive Property of multiplication over addition?

To break down complex multiplications into simpler parts Signup and view all the answers

What is the result of multiplying a whole number by 1?

The result is always the original number Signup and view all the answers

Why is estimating useful in calculations with whole numbers?

To get close to an answer without doing precise calculations Signup and view all the answers

What is the purpose of using a summary table for multiplication?

To practice and reinforce multiplication facts Signup and view all the answers

What is the result of multiplying a whole number by -1?

The result is always negative Signup and view all the answers

What is the purpose of rounding off numbers in calculations?

To simplify complex calculations Signup and view all the answers

What is the purpose of rounding off numbers in calculations?

To make calculations easier and faster Signup and view all the answers

What is the method of breaking down numbers into parts and adding each part separately?

Expanded Notation Signup and view all the answers

What is the result of subtracting a negative integer from a number?

The result is the same as adding the absolute value of the integer Signup and view all the answers

What is the purpose of carrying over in multiplication?

To write down the partial product and carry over extra values to the next column Signup and view all the answers

What is the method of aligning numbers vertically by their place values and adding each column?

Column Addition Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?

Long Division Signup and view all the answers

What is the technique of rearranging parts to make subtraction easier by borrowing from higher place values?

Borrowing Technique Signup and view all the answers

What is the method of subtracting numbers by aligning them by their place values and subtracting each column?

Column Subtraction Signup and view all the answers

What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?

Multiplication in Parts Signup and view all the answers

What is the purpose of scaling quantities in recipes?

To increase or decrease the quantity of ingredients based on the number of servings Signup and view all the answers

How can you calculate the profit percentage of an item?

By finding the difference between the selling price and the cost price, dividing by the cost price, and multiplying by 100 Signup and view all the answers

What is the result of adding a positive integer and a negative integer?

Depends on the absolute values of the integers Signup and view all the answers

How can you calculate the simple interest on an investment?

By multiplying the principal by the rate and time, and dividing by 100 Signup and view all the answers

What is the result of multiplying two negative integers?

Always positive Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

How can you calculate the discount amount of an item?

By multiplying the marked price by the discount rate, and subtracting the discount from the marked price Signup and view all the answers

What is the purpose of comparing ratios?

To determine which shapes or objects are more similar Signup and view all the answers

What is the effect of subtracting a negative integer from a number?

It increases the value Signup and view all the answers

How can you increase a quantity in a ratio?

By multiplying the quantity by the factor needed to reach the desired ratio Signup and view all the answers

What is the product of a positive integer and a negative integer?

A negative integer Signup and view all the answers

What property of integers allows flexibility in computation and simplification?

All of the above Signup and view all the answers

What is the result of subtracting a negative integer from a number?

Always increases the value Signup and view all the answers

What is the purpose of finding the absolute value of an integer?

To find the distance between the number and zero on the number line Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

A negative integer Signup and view all the answers

What is the result of multiplying a positive integer by -1?

A negative integer Signup and view all the answers

Which of the following properties states that the order of the numbers does not change the sum in addition?

Commutative Property Signup and view all the answers

What is the purpose of the Distributive Property of integers?

To simplify complex calculations Signup and view all the answers

What is the result of adding two positive integers?

A positive integer Signup and view all the answers

What is the purpose of the additive inverse in integer operations?

To find the sum of a number and its negative counterpart Signup and view all the answers

What is the result of subtracting a negative integer from a positive integer?

A positive integer Signup and view all the answers

What is the result of subtracting a larger integer from a smaller one?

A negative integer Signup and view all the answers

Which property allows multiplication to distribute over addition?

Distributive Property Signup and view all the answers

What is the result of multiplying two integers with the same sign?

A positive integer Signup and view all the answers

What is the result of adding two negative integers?

A negative integer Signup and view all the answers

What is the result of dividing a positive integer by a negative integer?

A negative integer Signup and view all the answers

Which property states that changing the grouping of numbers does not change the product in multiplication?

Associative Property Signup and view all the answers

What is the result of multiplying a negative integer by -1?

A positive integer Signup and view all the answers

Which property states that adding zero to any number does not change the value of that number?

Identity Property Signup and view all the answers

What is the purpose of the absolute value of an integer?

To find the distance between the number and zero on the number line Signup and view all the answers

What is the least common multiple (LCM) used for in adding or subtracting fractions?

Converting fractions to have a common denominator Signup and view all the answers

What is the formula to simplify a fraction?

a / b = a ÷ GCD(a, b) / b ÷ GCD(a, b) Signup and view all the answers

How do you convert a fraction to a decimal?

Divide the numerator by the denominator Signup and view all the answers

What is the result of multiplying two fractions together?

The product of the numerators divided by the product of the denominators Signup and view all the answers

How do you divide a fraction by another fraction?

Multiply the fraction by the reciprocal of the other fraction Signup and view all the answers

What is the term for a fraction that represents a part of a whole?

Fraction of a fraction Signup and view all the answers

What is the purpose of finding the greatest common divisor (GCD) in simplifying fractions?

To divide both the numerator and denominator by their GCD Signup and view all the answers

What is the formula to convert a fraction to a percentage?

Percentage = (a / b) × 100 Signup and view all the answers

What is the term for a fraction that combines a whole number with a fraction?

Mixed number Signup and view all the answers

What is the purpose of equivalent fractions?

To represent the same value even though they may look different Signup and view all the answers

What is the purpose of finding the prime factorization of a number?

To express the number as a product of its prime factors Signup and view all the answers

What is the difference between a prime number and a composite number?

A prime number has exactly two factors, while a composite number has more than two factors Signup and view all the answers

What is the purpose of finding the highest common factor (HCF) of two numbers?

To simplify fractions to their lowest terms Signup and view all the answers

How do you determine if a number is prime?

By checking if it can be divided evenly by any number smaller than its square root Signup and view all the answers

What is the purpose of finding the least common multiple (LCM) of two numbers?

To find a common denominator for adding fractions Signup and view all the answers

What is the formula for calculating distance?

Distance = Speed × Time Signup and view all the answers

What is the purpose of expressing a ratio?

To compare two quantities Signup and view all the answers

What is the result of dividing a number by its highest common factor (HCF)?

The result is always simplified Signup and view all the answers

What is the purpose of finding the multiples of a number?

To identify the sequence of numbers formed by multiplying the number by an integer Signup and view all the answers

What is the purpose of calculating the rate of a process?

To find the time required to complete the process Signup and view all the answers

What is the formula to calculate a fraction of a fraction?

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ Signup and view all the answers

How do you simplify a fraction?

Divide both the numerator and denominator by their greatest common divisor (GCD) Signup and view all the answers

What is the formula to convert a fraction to a percentage?

$\frac{a}{b} \times 100$ Signup and view all the answers

What is the formula to find the percentage of a given number?

$\left(\frac{\text{Percentage}}{100}\right) \times \text{Number}$ Signup and view all the answers

How do you increase a number by a percentage?

Calculate the percentage of the number and add it to the original number Signup and view all the answers

What is the formula to calculate percentage change?

$\left(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}}\right) \times 100$ Signup and view all the answers

What is the formula to convert a percentage to a fraction?

$\frac{\text{Percentage}}{100}$ Signup and view all the answers

How do you decrease a number by a percentage?

Calculate the percentage of the number and subtract it from the original number Signup and view all the answers

What is the formula to find the reciprocal of a fraction?

$\frac{b}{a}$ Signup and view all the answers

What is the method of comparing quantities using percentages?

Divide the part by the whole and multiply by 100 Signup and view all the answers

When adding decimal fractions, what is the correct step to follow?

Align the decimal points and then add or subtract as with whole numbers Signup and view all the answers

What is the purpose of converting decimal fractions to whole numbers in multiplication?

To eliminate the decimals Signup and view all the answers

When dividing a total amount by a certain number of people, what is the correct step to follow?

Convert the total amount to a decimal if necessary and divide Signup and view all the answers

What is the correct technique for multiplying decimal fractions?

Convert the decimals to whole numbers, multiply, and then adjust the decimal place Signup and view all the answers

What is the correct technique for dividing decimal fractions?

Convert the divisor to a whole number, divide, and then adjust the quotient Signup and view all the answers

What is the purpose of the associative property of addition?

To allow flexibility in the order of addition Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

What is the purpose of the commutative property of multiplication?

To allow flexibility in the order of multiplication Signup and view all the answers

What is the correct symbol for 'greater than' when comparing integers?

> Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

A negative integer Signup and view all the answers

What is the purpose of finding the equivalent fractions?

To compare the values of two fractions Signup and view all the answers

What is the process of converting a decimal to a fraction?

Write the decimal as a fraction with a denominator of a power of 10 and then simplify Signup and view all the answers

What is the distributive property used for in algebra?

To multiply a single term by each term within a parenthesis Signup and view all the answers

What is the purpose of simplifying algebraic expressions?

To combine like terms and eliminate any constants Signup and view all the answers

What is the result of multiplying two equivalent fractions?

A fraction with the same value as the original fractions Signup and view all the answers

What is the purpose of using the order of operations?

To follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction Signup and view all the answers

What is the result of simplifying a product expression?

A simplified expression with combined like terms Signup and view all the answers

What is the purpose of factoring in algebra?

To express an algebraic expression as a product of its factors Signup and view all the answers

What is the result of adding two equivalent decimals?

A decimal with the same value as the original decimals Signup and view all the answers

What is the purpose of using flow diagrams in algebra?

To visualize the sequence of operations Signup and view all the answers

What is the formula for calculating the nth triangular number?

$T_n = n(n+1)/2$ Signup and view all the answers

What is the relationship between the number of calls made and the airtime left on a cell phone?

The more calls made, the less airtime is left. Signup and view all the answers

What is the term for different expressions that represent the same value or relationship?

Equivalent forms Signup and view all the answers

What is the result of multiplying a negative integer and a negative integer?

Positive Signup and view all the answers

What is the purpose of flow diagrams in mathematics?

To show the relationships between variables Signup and view all the answers

What is the purpose of expressing a number in scientific notation?

To write the number as a product of a number between 1 and 10 and a power of 10 Signup and view all the answers

What is the result of squaring a fraction?

A new fraction where both the numerator and the denominator are squared Signup and view all the answers

What is the formula for calculating the nth term of a pattern that follows a geometric progression?

$T_n = T_1 \cdot r^{(n-1)}$ Signup and view all the answers

What is the relationship between the number of learners at a school and the number of classrooms needed?

More learners require more classrooms. Signup and view all the answers

What is the property of multiplication that states that multiplication distributes over addition and subtraction?

Distributive Property Signup and view all the answers

What is the purpose of describing calculations in words?

To explain the reasoning behind a calculation Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

What is the purpose of using the Laws of Exponents?

To simplify expressions Signup and view all the answers

What is the formula for calculating the nth term of a pattern that follows an arithmetic progression?

$T_n = T_1 + (n-1)d$ Signup and view all the answers

What is the relationship between the number of matches in an arrangement and the number of triangles in the arrangement?

More matches can create more triangles in specific patterns. Signup and view all the answers

What is the result of cubing a fraction?

A new fraction where both the numerator and the denominator are cubed Signup and view all the answers

What is the purpose of using exponents?

To write a product of the same integer in a concise manner Signup and view all the answers

What is the purpose of finding a specific value of one quantity linked to a value of another quantity?

To identify the connection between two quantities Signup and view all the answers

What is the result of subtracting a negative integer from a number?

The number increases Signup and view all the answers

What is the purpose of comparing numbers in scientific notation?

To compare the exponents and then the base numbers Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

Which of the following statements is true about closed number sentences?

They contain only known constants Signup and view all the answers

What is the purpose of using the distributive property of multiplication over addition?

To simplify calculations by breaking down multiplication into smaller parts Signup and view all the answers

What is the formula for the nth term of a sequence with a constant difference?

T_n = T_1 + (n - 1) * d Signup and view all the answers

What is the effect of adding a negative integer to a number?

It decreases the value Signup and view all the answers

What is the purpose of using the associative property of addition?

To simplify calculations by allowing us to add numbers in any order Signup and view all the answers

What is the result of subtracting a negative integer from a number?

It increases the value Signup and view all the answers

What is the formula for the nth term of a sequence with a constant ratio?

T_n = T_1 * r^(n-1) Signup and view all the answers

What is the purpose of using the commutative property of addition?

To simplify calculations by allowing us to add numbers in any order Signup and view all the answers

What is the result of multiplying two integers with the same sign?

A positive integer Signup and view all the answers

What is the result of multiplying a number by 1?

The result is always the number itself Signup and view all the answers

What is the purpose of using the commutative property of addition?

To change the order of numbers in an addition problem Signup and view all the answers

Which of the following properties does not apply to subtraction and division?

Commutative Property Signup and view all the answers

What is the result of adding 0 to a number?

The result is always the number itself Signup and view all the answers

What is the purpose of using the distributive property of multiplication over addition?

To break down complex multiplication into simpler parts Signup and view all the answers

What is the benefit of using the associative property of multiplication?

It allows us to group numbers in different ways to simplify the problem Signup and view all the answers

What is the purpose of estimating in calculations with whole numbers?

To get an approximate answer Signup and view all the answers

What is the benefit of using a summary table for multiplication?

It helps in practicing and reinforcing multiplication of various numbers Signup and view all the answers

What is the process of finding the prime factors of a number?

Prime factorization Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the purpose of finding the least common multiple (LCM) of two numbers?

To find the smallest multiple that two or more numbers have in common Signup and view all the answers

What is the process of finding the highest common factor (HCF) of two numbers?

Find the lowest power of each prime factor that appears in the factorization of each number Signup and view all the answers

What is the ratio of the number of hours worked by two people if they are paid $120 and $90, respectively?

4:3 Signup and view all the answers

What is the formula to calculate the distance traveled by an object?

Distance = Speed × Time Signup and view all the answers

What is the purpose of calculating the time required to process a certain amount based on a rate?

To determine the time required to process a certain amount Signup and view all the answers

What is the term for a natural number greater than 1 that can be formed by multiplying two smaller natural numbers?

Composite number Signup and view all the answers

What is the process of dividing quantities in a given ratio?

Sharing based on work done Signup and view all the answers

What is the term for describing how one quantity changes in relation to another?

Rate Signup and view all the answers

What is the value of the expression 5 + (-5)?

0 Signup and view all the answers

What is the result of subtracting a negative integer from a positive integer?

A larger value Signup and view all the answers

What is the product of a positive integer and a negative integer?

Always negative Signup and view all the answers

What is the purpose of the distributive property of multiplication?

To simplify multiplication over addition and subtraction Signup and view all the answers

What is the primary purpose of rounding off numbers in calculations?

To make calculations easier and faster Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

What is the advantage of using the multiplication in parts method?

It helps in breaking down complex multiplications into simpler parts Signup and view all the answers

What is the purpose of compensating in calculations?

To adjust for errors introduced by rounding Signup and view all the answers

What is the effect of subtracting a positive integer from a number?

Decreases the value Signup and view all the answers

What is the method of adding numbers by breaking down each number into its components?

Expanded Notation Signup and view all the answers

What is the property of addition that allows flexibility in computation and simplification?

All of the above Signup and view all the answers

What is the result of multiplying two negative integers?

A positive value Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the purpose of comparing integers using greater than or equal to?

To determine the relationship between two integers Signup and view all the answers

What is the purpose of the borrowing technique in subtraction?

To make subtraction easier Signup and view all the answers

What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?

Multiplication in Parts Signup and view all the answers

What is the property of multiplication that allows changing the order of the numbers?

Commutative property Signup and view all the answers

What is the purpose of carrying over in multiplication?

To write down the partial product and carry over extra values to the next column Signup and view all the answers

What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?

Step-by-Step Division Signup and view all the answers

What is the advantage of using the column addition method?

It helps in adding numbers with multiple digits Signup and view all the answers

Which of the following properties of integers states that changing the order of the numbers does not change the sum?

Commutative Property Signup and view all the answers

What is the result of adding a positive integer and its additive inverse?

Zero Signup and view all the answers

Which of the following properties of integers allows flexibility in computation and simplification?

All of the above Signup and view all the answers

What is the result of multiplying two integers with different signs?

A negative integer Signup and view all the answers

What is the purpose of the Distributive Property of integers?

To simplify calculations involving multiplication Signup and view all the answers

What is the result of adding two negative integers?

A negative integer Signup and view all the answers

Which of the following properties of integers states that changing the grouping of the numbers does not change the product?

Associative Property Signup and view all the answers

What is the absolute value of an integer?

The distance between the number and zero on the number line Signup and view all the answers

What is the result of subtracting a positive integer from another positive integer?

A positive integer Signup and view all the answers

What is the purpose of equivalent fractions?

To represent the same value in different ways Signup and view all the answers

What is the purpose of scaling quantities in recipes?

To use the ratio of ingredients to the number of servings Signup and view all the answers

How do you calculate the profit percentage?

By finding the difference between the selling price and the cost price, dividing by the cost price, and multiplying by 100 Signup and view all the answers

What is the result of adding a negative integer to a positive integer?

The result is positive if the positive integer is greater, otherwise negative Signup and view all the answers

How do you find the value of one part when dividing quantities in a ratio?

By summing the parts of the ratio and dividing the total quantity by the sum of the parts Signup and view all the answers

What is the formula for calculating simple interest?

Interest = Principal × Rate × Time Signup and view all the answers

What is the result of multiplying two negative integers?

The result is always positive Signup and view all the answers

What is the purpose of calculating the discount amount?

To find the selling price of an article Signup and view all the answers

What is the absolute value of an integer?

The distance between the number and zero on the number line Signup and view all the answers

What is the result of subtracting a positive integer from a negative integer?

The result is always negative Signup and view all the answers

How do you calculate the selling price of an article after a discount?

By subtracting the discount amount from the marked price Signup and view all the answers

What is the correct step to add or subtract decimal fractions?

Align decimal points and add or subtract as with whole numbers, then adjust the decimal point Signup and view all the answers

How do you multiply decimal fractions?

Convert decimals to whole numbers, multiply, and then adjust the decimal place Signup and view all the answers

What is the correct step to divide a decimal fraction by another decimal fraction?

Convert the divisor to a whole number, divide, and then adjust the decimal place Signup and view all the answers

What is the purpose of converting decimal fractions to whole numbers in multiplication?

To simplify the calculation by eliminating decimals Signup and view all the answers

What is the result of multiplying a positive integer by a negative integer?

A negative integer Signup and view all the answers

What is the property of integers that allows flexibility in computation and simplification?

Commutative property of addition Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

Zero Signup and view all the answers

What is the effect of subtracting a positive integer from a number?

The result is the same as adding the additive inverse Signup and view all the answers

What is the purpose of using exponential form in comparing and representing numbers?

To compare and represent numbers in a more concise and efficient manner Signup and view all the answers

What is the symbol used to indicate 'greater than' in comparing integers?

> Signup and view all the answers

What is the first step when adding or subtracting fractions with different denominators?

Find the least common multiple of the denominators Signup and view all the answers

What is the result of multiplying a fraction by its reciprocal?

A fraction with a numerator of 1 and a denominator of 1 Signup and view all the answers

What is the result of multiplying two integers with different signs?

The result is always negative. Signup and view all the answers

What is the purpose of using exponential form?

To simplify calculations involving powers. Signup and view all the answers

What is the purpose of simplifying a fraction?

To reduce the fraction to its simplest form, where the numerator and denominator are as small as possible Signup and view all the answers

What is the result of raising a number to the power of zero?

The result is always one. Signup and view all the answers

What is the formula for converting a fraction to a percentage?

Percentage = (a / b) × 100 Signup and view all the answers

What is the formula for adding fractions with different denominators?

(a / b) + (c / d) = (a × d + b × c) / (b × d) Signup and view all the answers

What is the rule for dividing powers with the same base?

Subtract the exponents. Signup and view all the answers

What is the result of multiplying a fraction by a whole number?

A fraction with a numerator equal to the product of the original numerator and the whole number, and a denominator equal to the original denominator Signup and view all the answers

What is the result of cubing a fraction?

The result is a new fraction where both the numerator and the denominator are cubed. Signup and view all the answers

What is the purpose of dividing a fraction by its greatest common divisor?

To reduce the fraction to its simplest form, where the numerator and denominator are as small as possible Signup and view all the answers

What is the purpose of scientific notation?

To express very large or very small numbers in a more compact form. Signup and view all the answers

What is the formula for multiplying fractions?

(a / b) × (c / d) = (a × c) / (b × d) Signup and view all the answers

What is the result of adding a positive integer to its additive inverse?

The result is always zero. Signup and view all the answers

What is the law of exponents that states that any number raised to the power of zero is one?

Power of Zero. Signup and view all the answers

What is the result of dividing a fraction by a whole number?

A fraction with a numerator equal to the original numerator divided by the whole number, and a denominator equal to the original denominator Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

The result is always negative. Signup and view all the answers

What is the formula for finding a fraction of a fraction?

(a / b) × (c / d) = (a × c) / (b × d) Signup and view all the answers

What is the result of subtracting a negative integer from another integer?

It has the same effect as adding its additive inverse. Signup and view all the answers

What is the purpose of the commutative property of multiplication?

To allow flexibility in the order of multiplication. Signup and view all the answers

What is the property of multiplication that states that changing the order of the numbers does not change the product?

Commutative Property Signup and view all the answers

What is the formula for the nth term in a sequence with a constant difference?

Tn = T1 + (n - 1) × d Signup and view all the answers

What is the result of adding an integer and its additive inverse?

It always equals 0. Signup and view all the answers

What is the purpose of using the distributive property of multiplication?

To simplify calculations by breaking down multiplication into smaller parts. Signup and view all the answers

What is the formula for the nth term in a sequence with a linear relationship?

Tn = a × n + b Signup and view all the answers

What is the result of multiplying a positive integer and a negative integer?

It is always negative. Signup and view all the answers

What is the effect of adding a positive integer to a number?

It always increases the value. Signup and view all the answers

What is the property of integers that allows flexibility in computation and simplification?

Additive Inverses Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the formula for the number of elements in the nth position of a triangular number sequence?

Tn = n*(n+1)/2 Signup and view all the answers

What is the relationship between the number of identical houses to be built and the number of bricks required?

More houses require more bricks Signup and view all the answers

What is the purpose of a flow diagram in mathematics?

To show the calculations needed to produce output numbers Signup and view all the answers

What is the term for different expressions that represent the same value or relationship?

Equivalent forms Signup and view all the answers

What is the formula to find a fraction of a fraction?

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ Signup and view all the answers

What is the formula for the number of elements in the nth position of a square number sequence?

Tn = n^2 Signup and view all the answers

What is the process of simplifying a fraction?

Dividing both the numerator and denominator by their greatest common divisor Signup and view all the answers

What is the relationship between the number of learners at a school and the number of classrooms needed?

More learners require more classrooms Signup and view all the answers

What is the formula for the number of elements in the nth position of a T-shaped number sequence that follows an arithmetic progression?

Tn = T1 + (n - 1) * d Signup and view all the answers

How do you convert a percentage to a fraction?

Write the percentage as a fraction with 100 as the denominator Signup and view all the answers

What is the relationship between the number of calls you make and the airtime left on your cell phone?

The more calls you make, the less airtime you have left Signup and view all the answers

What is the formula to find the percentage change?

$\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$ Signup and view all the answers

What is the method of finding the percentage of a given number?

Convert the percentage to a fraction and multiply by the number Signup and view all the answers

What is the term for a variable quantity that is influenced by another variable quantity?

Dependent variable Signup and view all the answers

What is the purpose of finding the relationships between variables in mathematics?

To find a specific value of one quantity linked to a value of the other quantity Signup and view all the answers

What is the formula to find the increased value of a number by a percentage?

$\text{Original Number} + \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right)$ Signup and view all the answers

What is the method of comparing quantities using percentages?

Divide the part by the whole and multiply by 100 Signup and view all the answers

What is the formula to find the decimal equivalent of a fraction?

Divide the numerator by the denominator Signup and view all the answers

What is the method of converting a fraction to a percentage?

Divide the numerator by the denominator and multiply by 100 Signup and view all the answers

What is the formula to find the reciprocal of a fraction?

$\frac{a}{b} = \frac{b}{a}$ Signup and view all the answers

What is the process of finding an equivalent fraction in its simplest form?

Simplifying fractions Signup and view all the answers

Which of the following is an example of an equivalent algebraic expression?

2x + 3x Signup and view all the answers

What is the purpose of using the distributive property of multiplication over addition?

To simplify algebraic expressions Signup and view all the answers

What is the result of dividing a numerator by a denominator to convert a fraction to a decimal?

An equivalent decimal Signup and view all the answers

What is the purpose of combining like terms in an algebraic expression?

To simplify the expression Signup and view all the answers

What is the result of using the distributive property to expand a product expression?

A sum expression Signup and view all the answers

What is the purpose of using factoring in algebraic expressions?

To simplify expressions Signup and view all the answers

What is the result of converting a decimal to a fraction with a denominator of a power of 10?

An equivalent fraction Signup and view all the answers

What is the purpose of using the associative property of multiplication in algebraic expressions?

To simplify expressions Signup and view all the answers

What is the result of simplifying a quotient expression involving division?

A simplified algebraic expression Signup and view all the answers

What is the definition of an equation?

A mathematical statement that asserts the equality of two expressions Signup and view all the answers

What is the purpose of solving an equation?

To find the value(s) of the variable(s) that make the equation true Signup and view all the answers

What is the definition of additive inverses?

Numbers that add up to zero Signup and view all the answers

What is the sum of angles on a straight line?

180° Signup and view all the answers

What is the formula for angles on a straight line?

∠1 + ∠2 + ∠3 = 180° Signup and view all the answers

What is the definition of supplementary angles?

Angles that add up to 180° Signup and view all the answers

What is the process of solving an equation by finding the original value of the variable that produces a given result?

Undoing Signup and view all the answers

What is the definition of multiplicative inverses?

Numbers that multiply to give one Signup and view all the answers

What is the key property of vertically opposite angles?

They are always equal Signup and view all the answers

When two lines are intersected by a transversal, which of the following angles are equal?

Corresponding and alternate interior angles Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is the property of co-interior angles when two lines are intersected by a transversal?

They are supplementary Signup and view all the answers

What is the characteristic of a rhombus?

All sides are equal with opposite equal angles Signup and view all the answers

What is the definition of a scalene triangle?

A triangle with all sides and angles different Signup and view all the answers

What is the term for a polygon with all sides and angles equal?

Regular polygon Signup and view all the answers

What is the distance from the center to any point on the circle?

Radius Signup and view all the answers

What is the formula for alternate interior angles when two lines are intersected by a transversal?

∠d = ∠f Signup and view all the answers

What is the process of creating precise figures using specific tools and methods?

Constructing 2D shapes Signup and view all the answers

What is the definition of a rectangle?

A quadrilateral with opposite sides equal and four right angles Signup and view all the answers

How do you construct a 60° angle?

By drawing an equilateral triangle and using its properties Signup and view all the answers

What is the key property of corresponding angles when two lines are intersected by a transversal?

They are always equal Signup and view all the answers

What is the formula for co-interior angles when two lines are intersected by a transversal?

∠c + ∠f = 180° Signup and view all the answers

What is the term for a line segment within the circle that touches two points?

Chord Signup and view all the answers

What is the definition of an equilateral triangle?

A triangle with all sides and angles equal Signup and view all the answers

What is the method of constructing a triangle given three sides?

Using a compass to measure and draw sides Signup and view all the answers

What is the sum of the interior angles of a triangle?

180° Signup and view all the answers

What is the term for a region bounded by two radii and an arc?

Sector Signup and view all the answers

How do you construct a perpendicular bisector?

Using a compass to create two arcs from the endpoints of a line segment Signup and view all the answers

What is the defining property of a parallelogram?

Opposite sides are equal and parallel Signup and view all the answers

What is the term for the angle subtended by an arc at the center of a circle?

Central angle Signup and view all the answers

What is the method of constructing a quadrilateral given specific properties?

Using a combination of techniques for constructing angles, sides, and parallel lines Signup and view all the answers

What is the process of applying theorems to prove properties of geometric figures?

Using theorems and proofs Signup and view all the answers

What is the term for a quadrilateral inscribed in a circle?

Cyclic quadrilateral Signup and view all the answers

What is the result of applying the Pythagorean theorem to a right triangle?

The square of the hypotenuse is equal to the sum of the squares of the other two sides Signup and view all the answers

What is the primary purpose of using the problem-solving steps in geometry?

To visualize the problem and identify the geometric figures involved Signup and view all the answers

What is the purpose of identifying geometric figures in problem-solving?

To apply theorems and properties Signup and view all the answers

What is the main difference between congruent and similar shapes?

Congruent shapes have the same size, but similar shapes do not Signup and view all the answers

What is the term for the line that bisects an angle in a circle?

Radius Signup and view all the answers

Which of the following is a criterion for congruent triangles?

Side-Side-Side Signup and view all the answers

What is the result of applying the angle sum property of a quadrilateral?

The sum of the interior angles is 360° Signup and view all the answers

What is the purpose of using theorems and properties in geometry?

To prove properties of geometric figures Signup and view all the answers

What is the purpose of using diagrams in problem-solving?

To visualize the problem and identify the geometric figures involved Signup and view all the answers

Which of the following is a property of congruent shapes?

Corresponding angles and sides are equal Signup and view all the answers

What is the purpose of proving congruence in geometric problems?

To construct logical arguments to show that two shapes are congruent Signup and view all the answers

Which of the following is a criterion for similar triangles?

Angle-Angle Signup and view all the answers

What is the primary purpose of using theorems and properties in geometry?

To set up equations or logical statements Signup and view all the answers

What is the main advantage of using congruent shapes in real-world applications?

They can be used to design patterns and create tiling designs Signup and view all the answers

What is the purpose of verifying solutions in geometry?

To check the solutions by substituting back into the original conditions Signup and view all the answers

What is the purpose of checking the scale in a graph?

To understand the range and intervals of the data Signup and view all the answers

What type of graph is used to show the relationship between two variables?

Scatter plot Signup and view all the answers

What is the formula for the Pythagorean theorem?

c^2 = a^2 + b^2 Signup and view all the answers

What is the purpose of drawing a line of best fit in a scatter plot?

To show the correlation between the variables Signup and view all the answers

What is the term for the side opposite the right angle in a right-angled triangle?

Hypotenuse Signup and view all the answers

What is the purpose of using a title in a graph?

To provide a clear and descriptive summary of the data Signup and view all the answers

What is the type of triangle that has one angle greater than 90 degrees?

Obtuse-angled triangle Signup and view all the answers

What is the purpose of using a legend in a graph?

To include multiple datasets or colors Signup and view all the answers

What is the term for the leftover value when dividing a number?

Remainder Signup and view all the answers

What is the purpose of drawing a histogram?

To show the distribution of continuous data Signup and view all the answers

What is the primary criterion for determining if two shapes are similar?

They have the same shape but not necessarily the same size. Signup and view all the answers

What type of graph is used to represent categorical data with rectangular bars?

Bar Graph Signup and view all the answers

What is the purpose of using similarity in real-world applications?

To resize images and create proportional models Signup and view all the answers

What type of graph is used to display proportions and percentages as segments of a circle?

Pie Chart Signup and view all the answers

What is the purpose of using scale factors in solving problems with similar shapes?

To scale shapes up or down Signup and view all the answers

What type of graph is used to show relationships between two variables using points on a coordinate plane?

Scatter Plot Signup and view all the answers

What is the primary purpose of interpreting graphs?

To understand relationships between variables Signup and view all the answers

What is the purpose of using the property of similar shapes in geometric proofs?

To establish relationships between different parts of geometric figures Signup and view all the answers

What is the purpose of breaking down composite figures into simpler components?

To analyze and solve for unknowns Signup and view all the answers

What is the primary purpose of using graphs in real-world applications?

To understand relationships between variables and make predictions Signup and view all the answers

In a right-angled triangle, if the length of the hypotenuse is 5 units and one of the other sides is 3 units, what is the length of the other side?

√7 units Signup and view all the answers

What is the formula to find the perimeter of a rectangle with length l and breadth b?

P = 2(l + b) Signup and view all the answers

What is the circumference of a circle with a radius of 4 cm?

16π cm Signup and view all the answers

What is the area of a circle with a diameter of 14 cm?

49π cm² Signup and view all the answers

If the sum of the squares of two sides of a triangle is equal to the square of the third side, what can be concluded about the triangle?

The triangle is right-angled. Signup and view all the answers

What is the formula to find the area of a square with a side length of s?

A = s² Signup and view all the answers

What is the perimeter of a square with a side length of 5 cm?

20 cm Signup and view all the answers

What is the result of converting 1 m² to square centimeters?

10,000 cm² Signup and view all the answers

What is the formula to find the area of a triangle with a base of b and a height of h?

A = 1/2bh Signup and view all the answers

What is the purpose of the Pythagorean theorem?

To find the length of a side of a right-angled triangle Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2l + 2b Signup and view all the answers

What is the formula to calculate the area of a triangle?

A = 1/2 × base × height Signup and view all the answers

What is the formula to calculate the circumference of a circle?

C = 2πr Signup and view all the answers

What is the formula to calculate the area of a circle?

A = πr^2 Signup and view all the answers

How do you find the perimeter of a composite shape?

Break down the shape into simpler shapes and calculate their perimeters separately Signup and view all the answers

What is the unit of area?

Square metre Signup and view all the answers

How do you convert between square units?

By squaring the conversion factor Signup and view all the answers

What is the formula to calculate the area of a square?

A = s^2 Signup and view all the answers

What is the definition of a rhombus?

A quadrilateral with all sides of equal length and opposite equal angles Signup and view all the answers

What is the characteristic of a convex polygon?

All interior angles are less than 180 degrees Signup and view all the answers

What is the definition of a sector?

A region bounded by two radii and an arc Signup and view all the answers

What is the primary tool used to bisect an angle?

Compass Signup and view all the answers

How can you construct a 60° angle?

Drawing an equilateral triangle Signup and view all the answers

What is the technique used to construct perpendicular lines?

Using a ruler and set square Signup and view all the answers

How can you construct a quadrilateral with specific properties?

Using a combination of techniques for constructing angles, sides, and parallel lines Signup and view all the answers

What is the purpose of investigating geometric figures?

To examine the attributes, relationships, and characteristics of various shapes Signup and view all the answers

What is the definition of a kite?

A quadrilateral with two pairs of adjacent sides that are equal Signup and view all the answers

What is the purpose of constructing 2D shapes?

To create precise figures using specific tools and methods Signup and view all the answers

What is the purpose of solving an equation?

To find the value of a variable that makes the equation true Signup and view all the answers

What is the definition of an additive inverse?

A number that adds up to zero Signup and view all the answers

What is the sum of angles on a straight line?

180° Signup and view all the answers

What is the process of finding the value of a variable by undoing the operation performed on it?

Undoing an operation Signup and view all the answers

What is the purpose of using additive inverses in solving equations?

To move constants to the other side of the equation Signup and view all the answers

What is the definition of supplementary angles?

Angles that add up to 180° Signup and view all the answers

What is the purpose of using multiplicative inverses in solving equations?

To solve for the variable Signup and view all the answers

What is the formula for angles on a straight line?

∠1 + ∠2 + ∠3 = 180° Signup and view all the answers

What is the key property of vertically opposite angles?

They are always equal. Signup and view all the answers

What is the relationship between corresponding angles when two lines are parallel?

They are equal. Signup and view all the answers

What is the formula for alternate interior angles when two lines are parallel?

Angle d = Angle f Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is the definition of a scalene triangle?

A triangle with all sides and angles different. Signup and view all the answers

What is the property of co-interior angles when two lines are parallel?

They are supplementary. Signup and view all the answers

What is the formula for alternate exterior angles when two lines are parallel?

Angle a = Angle g Signup and view all the answers

What is the definition of a rectangle?

A quadrilateral with opposite sides equal and four right angles. Signup and view all the answers

What is the relationship between alternate exterior angles when two lines are parallel?

They are equal. Signup and view all the answers

What is the key property of a transversal?

It is a line that intersects at least two other lines. Signup and view all the answers

What is the sum of the interior angles of a triangle?

180° Signup and view all the answers

What is the name of the theorem that states that the sum of the interior angles of a triangle is 180°?

Triangle Sum Theorem Signup and view all the answers

What is the definition of a cyclic quadrilateral?

A quadrilateral inscribed in a circle Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is the definition of a parallelogram?

A quadrilateral with opposite sides equal and parallel Signup and view all the answers

What is the definition of a rhombus?

A quadrilateral with all sides equal Signup and view all the answers

What is the definition of a trapezium?

A quadrilateral with one pair of opposite sides parallel Signup and view all the answers

What is the definition of a circle?

A set of points equidistant from a fixed point Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr Signup and view all the answers

What is the definition of a tangent to a circle?

A line that intersects the circle at one point Signup and view all the answers

What is the definition of similar shapes?

Shapes that have the same shape but not necessarily the same size Signup and view all the answers

What is the purpose of identifying similar shapes?

To establish relationships between different parts of geometric figures Signup and view all the answers

What is the main difference between a bar graph and a histogram?

The type of data represented Signup and view all the answers

What is the purpose of a title in a graph?

To understand what the graph is about Signup and view all the answers

What is the purpose of a scatter plot?

To show the relationship between two variables Signup and view all the answers

What is the purpose of scale factors in solving problems involving similar shapes?

To determine the proportionality of corresponding sides Signup and view all the answers

What is the purpose of using the property of corresponding angles in similar shapes?

To apply the property that corresponding angles of similar shapes are equal Signup and view all the answers

What is the purpose of interpreting graphs in real-world applications?

To understand relationships between variables and make predictions Signup and view all the answers

What is the purpose of using criteria such as AA, SAS, and SSS to determine if two shapes are similar?

To check for proportionality of corresponding sides and equality of corresponding angles Signup and view all the answers

What is the purpose of combining congruence and similarity in geometric proofs?

To establish relationships between different parts of geometric figures Signup and view all the answers

What is the purpose of checking the scale when drawing graphs?

To understand the range and intervals of the data Signup and view all the answers

What type of graph is used to show the relationship between two variables?

Scatter plot Signup and view all the answers

What is the purpose of drawing a line of best fit in a scatter plot?

To show the correlation between the variables Signup and view all the answers

What is the definition of a right-angled triangle?

A triangle with one angle equal to 90 degrees Signup and view all the answers

What is the formula for the Pythagorean theorem?

c^2 = a^2 + b^2 Signup and view all the answers

What is the purpose of using a legend in a graph?

To provide additional information about the data Signup and view all the answers

What type of graph is used to show the proportion of each category?

Pie chart Signup and view all the answers

What is the importance of double-checking data values and calculations before plotting a graph?

To ensure the accuracy of the data Signup and view all the answers

What is the purpose of using a title in a graph?

To summarize the main idea of the graph Signup and view all the answers

What type of triangle has one angle greater than 90 degrees?

Obtuse-angled triangle Signup and view all the answers

What is the primary difference between similar and congruent shapes?

Similar shapes have the same shape but not necessarily the same size, while congruent shapes have the same shape and size. Signup and view all the answers

Which of the following is a criterion for congruent triangles?

All of the above Signup and view all the answers

What is the purpose of proving congruence in geometric problems?

To justify the equality of sides and angles Signup and view all the answers

Which of the following is a property of similar shapes?

Corresponding angles are equal, and corresponding sides are in proportion. Signup and view all the answers

What is the first step in solving a problem involving congruent shapes?

Identify the congruent shapes Signup and view all the answers

What is the result of applying the Angle-Angle-Side criterion for similar triangles?

The triangles are similar Signup and view all the answers

What is the purpose of using the problem-solving steps for congruent shapes?

To solve real-world problems involving congruent shapes Signup and view all the answers

Which of the following is a characteristic of congruent shapes?

All corresponding sides and angles are equal Signup and view all the answers

What is the outcome of applying the Side-Side-Side criterion for congruent triangles?

The triangles are congruent Signup and view all the answers

What is the primary application of congruent shapes in real-world problems?

Designing patterns and creating tiling designs Signup and view all the answers

What is the formula to calculate the area of a square?

A = s^2 Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2l + 2b Signup and view all the answers

What is the relationship between the sides of an obtuse-angled triangle?

a^2 + b^2 < c^2 Signup and view all the answers

What is the formula to calculate the circumference of a circle?

C = 2πr Signup and view all the answers

What is the formula to find the length of the hypotenuse or any side of a right-angled triangle?

c = √(a^2 + b^2) Signup and view all the answers

What is the formula to calculate the area of a triangle?

A = (1/2) × base × height Signup and view all the answers

What is the converse of the Pythagorean theorem?

If a^2 + b^2 = c^2, the triangle is right-angled. Signup and view all the answers

What is the formula to find the perimeter of a rectangle?

P = 2(l + b) Signup and view all the answers

What is the process of breaking down a composite shape into simpler shapes and calculating their areas separately?

Composition Signup and view all the answers

What is the unit of measurement for the area of a shape?

cm² Signup and view all the answers

What is the formula to find the area of a circle?

A = πr^2 Signup and view all the answers

What is the formula to calculate the area of a circle?

A = πr^2 Signup and view all the answers

What is the purpose of converting between square units?

To understand the relationship between units Signup and view all the answers

What is the process of converting between units of length?

Conversion Signup and view all the answers

What is the formula to find the circumference of a circle?

C = 2πr Signup and view all the answers

What is the purpose of using the Pythagorean theorem?

To find the length of the hypotenuse or any side of a right-angled triangle Signup and view all the answers

What is the formula to find the area of a rectangle?

A = l × b Signup and view all the answers

What is the purpose of estimating in calculations?

To get an approximate value of a quantity Signup and view all the answers

What is the definition of a rhombus?

A quadrilateral with all sides equal and opposite equal angles Signup and view all the answers

What is the name of the line segment within a circle that touches two points?

Chord Signup and view all the answers

What is the purpose of constructing 2D shapes?

To create precise figures using specific tools and methods Signup and view all the answers

What is the name of the technique used to divide an angle into two equal parts?

Bisecting an angle Signup and view all the answers

What is the name of the region bounded by two radii and an arc?

Sector Signup and view all the answers

What is the purpose of investigating properties of geometric figures?

To examine the attributes, relationships, and characteristics of various shapes Signup and view all the answers

What is the name of the polygon with all sides and angles equal?

Regular polygon Signup and view all the answers

What is the name of the technique used to draw a line perpendicular to a given line?

Drawing a perpendicular bisector Signup and view all the answers

What is the name of the region bounded by a chord and an arc?

Segment Signup and view all the answers

What is the definition of an equation?

A mathematical statement that asserts the equality of two expressions. Signup and view all the answers

What is the purpose of solving an equation?

To find the value of the variable that makes the equation true. Signup and view all the answers

What is the method of solving an equation by inspecting the equation?

Substituting a specific value of x into the equation to check if it is true. Signup and view all the answers

What is the sum of angles on a straight line?

180° Signup and view all the answers

What is the sum of the interior angles of a triangle?

180° Signup and view all the answers

What is the characteristic of a quadrilateral with one pair of opposite sides parallel?

Trapezium Signup and view all the answers

What is the definition of additive inverses?

Numbers that add up to zero. Signup and view all the answers

What is the purpose of using inverse operations to solve an equation?

To isolate the variable on one side of the equation. Signup and view all the answers

What is the angle subtended by an arc at the center of a circle?

Twice the angle subtended at any point on the circumference Signup and view all the answers

What is the definition of doing in the context of equations?

Evaluating an expression by substituting a variable with a value. Signup and view all the answers

What is the process of using geometric tools to construct shapes accurately?

Construction and Measurement Signup and view all the answers

What is the term for a quadrilateral with opposite sides equal and parallel?

Parallelogram Signup and view all the answers

What is the definition of undoing in the context of equations?

Solving an equation by finding the original value of the variable. Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is the type of triangle with two equal sides?

Isosceles Signup and view all the answers

What is the term for a line that touches a circle at a single point?

Tangent Signup and view all the answers

What is the process of solving geometric problems by applying properties and theorems to find unknown measurements?

Problem Solving Signup and view all the answers

What is the type of quadrilateral with all sides equal and opposite angles equal?

Rhombus Signup and view all the answers

What is the relationship between vertically opposite angles?

They are always equal Signup and view all the answers

What is the formula for alternate interior angles when two lines are parallel?

∠d = ∠f Signup and view all the answers

What is the sum of the interior angles of any quadrilateral?

360° Signup and view all the answers

What is the definition of a rectangle?

A quadrilateral with opposite sides equal and four right angles Signup and view all the answers

What is the formula for co-interior angles when two lines are parallel?

∠c + ∠f = 180° Signup and view all the answers

What type of angle is formed when a transversal intersects two lines?

Vertically opposite angle Signup and view all the answers

What is the property of corresponding angles when two lines are parallel?

They are always equal Signup and view all the answers

What is the definition of an equilateral triangle?

A triangle with all sides and angles equal Signup and view all the answers

What is the relationship between alternate exterior angles when two lines are parallel?

They are always equal Signup and view all the answers

What is the formula for alternate exterior angles when two lines are parallel?

∠a = ∠g Signup and view all the answers

What is the key characteristic of congruent shapes?

They have the same shape and size. Signup and view all the answers

What is the result of superimposing two congruent shapes?

They overlap perfectly. Signup and view all the answers

What is the criterion for triangle congruence if all three sides of one triangle are equal to all three sides of another triangle?

SSS Signup and view all the answers

What is the purpose of using the SSS criterion in solving problems?

To prove congruence between two triangles. Signup and view all the answers

What is the definition of similar shapes?

Shapes with the same shape but different sizes. Signup and view all the answers

What is the property of similar shapes that states that corresponding angles are equal?

Corresponding angles are equal. Signup and view all the answers

What is the method of problem-solving involving congruent shapes?

Identify congruent shapes, use properties of congruent shapes, and prove congruence. Signup and view all the answers

What is the purpose of using congruent shapes in real-world applications?

To design patterns and create tiling designs. Signup and view all the answers

What is the criterion for triangle similarity if two angles of one triangle are equal to two angles of another triangle?

AA Signup and view all the answers

What is the result of scaling a shape?

A similar shape with a different size. Signup and view all the answers

What is the definition of similar shapes?

Two shapes with the same shape but not necessarily the same size, and all corresponding angles are equal and proportional sides Signup and view all the answers

What is the purpose of using scale factors in similar shapes?

To determine the scale factor between similar shapes and use it to calculate unknown side lengths or scale shapes up or down Signup and view all the answers

What is the main difference between a bar graph and a histogram?

A bar graph is used for categorical data, while a histogram is used for continuous data Signup and view all the answers

What can be inferred from a scatter plot?

The correlation between two variables Signup and view all the answers

What is the purpose of analyzing graphs?

To interpret the data and make predictions Signup and view all the answers

What is the formula for calculating the perimeter of a rectangle?

P = 2l + 2b Signup and view all the answers

What is the definition of a pie chart?

A graph that displays the proportion of a part to the whole Signup and view all the answers

What is the formula for calculating the area of a square?

A = s^2 Signup and view all the answers

What is the formula for calculating the circumference of a circle?

C = 2πr Signup and view all the answers

What is the purpose of using the property of similar shapes?

To apply the property that corresponding angles of similar shapes are equal, and use the proportionality of corresponding sides to find missing lengths Signup and view all the answers

What is the definition of a line graph?

A graph that shows trends over time by connecting data points with lines Signup and view all the answers

What is the formula for calculating the area of a circle?

A = πr^2 Signup and view all the answers

What is the main purpose of checking the scale in a graph?

To understand the range and intervals of data Signup and view all the answers

What is the method of breaking down composite shapes into simpler shapes and calculating their areas separately?

Breakdown of composite shapes Signup and view all the answers

What is the purpose of identifying similar shapes?

To use the property of similar shapes to solve problems Signup and view all the answers

Which type of graph is best suited for showing the relationship between two variables?

Scatter plot Signup and view all the answers

What is the unit of measurement for the area of a shape?

square units (mm², cm², m², km²) Signup and view all the answers

What is the definition of a composite figure?

A figure that is made up of two or more similar shapes Signup and view all the answers

What is the formula to find the length of the hypotenuse of a right-angled triangle?

c = sqrt(a^2 + b^2) Signup and view all the answers

What is the name of the theorem that states the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides in a right-angled triangle?

Theorem of Pythagoras Signup and view all the answers

What is the formula for calculating the perimeter of a square?

P = 4s Signup and view all the answers

What is the formula for calculating the area of a triangle?

A = 1/2bh Signup and view all the answers

What is the condition for a triangle to be right-angled?

a^2 + b^2 = c^2 Signup and view all the answers

What is the purpose of a title in a graph?

To provide a clear and descriptive title Signup and view all the answers

What is the formula to find the perimeter of a rectangle?

P = 2(l + b) Signup and view all the answers

What is the main difference between a bar graph and a histogram?

The spacing between the bars Signup and view all the answers

What is the formula to find the area of a circle?

A = πr^2 Signup and view all the answers

What is the purpose of using different colors or patterns in a pie chart?

To differentiate between categories Signup and view all the answers

What is the relationship between the diameter and radius of a circle?

d = 2r Signup and view all the answers

What is the name of the side opposite the right angle in a right-angled triangle?

Hypotenuse Signup and view all the answers

What is the purpose of drawing a trend line in a line graph?

To predict future values Signup and view all the answers

What is the formula to find the circumference of a circle?

C = 2πr Signup and view all the answers

What is the main purpose of using a legend in a graph?

To differentiate between datasets Signup and view all the answers

What is the purpose of using the Pythagorean theorem?

To find the length of the hypotenuse or any side of a right-angled triangle Signup and view all the answers

What is the condition for a triangle to be acute-angled?

a^2 + b^2 > c^2 Signup and view all the answers

What is the formula for calculating the length of the hypotenuse in a right-angled triangle?

c^2 = a^2 + b^2 Signup and view all the answers

What is the formula to find the area of a rectangle?

A = l × b Signup and view all the answers

What is the purpose of converting between square units?

To make calculations easier and more accurate Signup and view all the answers

What is the definition of vertically opposite angles?

Angles opposite each other when two lines intersect. Signup and view all the answers

What is the formula for co-interior angles?

∠c + ∠f = 180° Signup and view all the answers

What is the property of corresponding angles?

They are equal. Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is a characteristic of a rhombus?

All sides are equal with opposite equal angles Signup and view all the answers

What is the definition of an equilateral triangle?

A triangle with all sides and angles equal. Signup and view all the answers

What is the name of the region bounded by two radii and an arc?

Sector Signup and view all the answers

What is the formula for alternate interior angles?

∠a = ∠e Signup and view all the answers

What is the purpose of constructing angles?

To create precise figures using specific tools and methods Signup and view all the answers

What is the definition of a transversal?

A line that intersects at least two other lines. Signup and view all the answers

What is the property of alternate exterior angles?

They are equal. Signup and view all the answers

What is the name of the line segment within the circle that touches two points?

Chord Signup and view all the answers

What is the definition of a quadrilateral?

A two-dimensional shape with four sides and four angles. Signup and view all the answers

What is the process of creating a 60° angle?

Drawing an equilateral triangle and using its properties Signup and view all the answers

What is the definition of co-interior angles?

Angles on the same side of the transversal and inside the two lines. Signup and view all the answers

What is the purpose of identifying shapes?

All of the above Signup and view all the answers

What is the name of the line that passes through the midpoint of a line segment?

Perpendicular bisector Signup and view all the answers

What is the process of constructing a quadrilateral?

Using a combination of techniques for constructing angles, sides, and parallel lines Signup and view all the answers

What is the name of the angle created by bisecting an angle?

Equal angle Signup and view all the answers

What is the main purpose of solving an equation?

To find the value of a variable that makes the equation true Signup and view all the answers

What is the purpose of investigating properties of geometric figures?

To examine the attributes, relationships, and characteristics of various shapes Signup and view all the answers

What is the definition of an equation?

A mathematical statement that asserts the equality of two expressions Signup and view all the answers

What is the purpose of doing and undoing in equations?

To solve an equation by finding the original value of the variable Signup and view all the answers

What is the definition of additive inverses?

Numbers that add up to zero Signup and view all the answers

What is the formula for angles on a straight line?

∠1 + ∠2 + ∠3 = 180° Signup and view all the answers

What is the definition of supplementary angles?

Angles that add up to 180° Signup and view all the answers

What is the purpose of using additive inverses in solving equations?

To isolate the variable Signup and view all the answers

What is the definition of equivalent equations?

Equations that have the same solution Signup and view all the answers

What is the primary step in solving problems involving geometric figures?

Draw diagrams Signup and view all the answers

What is the definition of congruent shapes?

Shapes with the same shape and size Signup and view all the answers

What is the Side-Side-Side (SSS) criterion for congruent triangles?

If all three sides of one triangle are equal to all three sides of another triangle Signup and view all the answers

What is the purpose of using congruent shapes in real-world applications?

To design patterns and create tiling designs Signup and view all the answers

What is the definition of similar shapes?

Shapes with the same shape but not necessarily the same size Signup and view all the answers

What is the Angle-Angle (AA) criterion for similar triangles?

If two angles of one triangle are equal to two angles of another triangle Signup and view all the answers

What is the Side-Angle-Side (SAS) criterion for similar triangles?

If one angle of one triangle is equal to one angle of another triangle, and the sides including these angles are in proportion Signup and view all the answers

What is the purpose of using similar shapes in problem-solving?

To find the scale factor of similar shapes Signup and view all the answers

What is the result of applying the properties of congruent shapes?

Corresponding angles and sides are equal Signup and view all the answers

What is the importance of verifying solutions in problem-solving?

To ensure that the solution is correct and satisfies all given constraints Signup and view all the answers

What is the primary purpose of examining the scale of a graph?

To understand the range and intervals of the data Signup and view all the answers

Which type of graph is used to display categorical data?

Bar Graph Signup and view all the answers

What is the formula for the Pythagorean Theorem?

c^2 = a^2 + b^2 Signup and view all the answers

What is the purpose of using a legend in a graph?

To differentiate between multiple datasets or colors Signup and view all the answers

What type of triangle has one angle greater than 90 degrees?

Obtuse-angled triangle Signup and view all the answers

What is the purpose of using a title in a graph?

To provide a clear and descriptive title Signup and view all the answers

Which type of graph is used to display paired data for two variables?

Scatter Plot Signup and view all the answers

What is the longest side in a right-angled triangle?

Hypotenuse Signup and view all the answers

What is the purpose of drawing a histogram?

To display continuous data divided into intervals Signup and view all the answers

What is the purpose of using a legend in a scatter plot?

To differentiate between multiple datasets or colors Signup and view all the answers

What is the formula to calculate the area of a square?

A = s^2 Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2l + 2b Signup and view all the answers

What is the formula to calculate the area of a triangle?

A = 1/2 × base × height Signup and view all the answers

What is the formula to calculate the circumference of a circle?

C = 2πr Signup and view all the answers

What is the formula to calculate the area of a circle?

A = πr^2 Signup and view all the answers

How do you calculate the perimeter of a composite shape?

Break down the shape into simpler shapes, calculate their perimeters separately, and then sum them up. Signup and view all the answers

How do you calculate the area of a composite shape?

Break down the shape into simpler shapes, calculate their areas separately, and then sum them up. Signup and view all the answers

What is the purpose of converting between units in problems involving perimeter and area?

To make calculations easier and more accurate. Signup and view all the answers

What is the relationship between the sides of a right-angled triangle?

a^2 + b^2 = c^2 Signup and view all the answers

What is the formula to find the length of the hypotenuse of a right-angled triangle?

c = √(a^2 + b^2) Signup and view all the answers

What is the converse of the Pythagorean theorem?

If a^2 + b^2 = c^2, the triangle is right-angled. Signup and view all the answers

What is the formula to find the perimeter of a rectangle?

P = 2(l + b) Signup and view all the answers

What is the formula to find the area of a circle?

A = πr^2 Signup and view all the answers

What is the formula to find the circumference of a circle?

C = 2πr Signup and view all the answers

What is the conversion factor to convert square centimeters to square meters?

1 cm^2 = 0.01 m^2 Signup and view all the answers

What is the formula to find the area of a triangle?

A = ½bh Signup and view all the answers

What is the perimeter of a square with side length 4 cm?

16 cm Signup and view all the answers

What is the area of a rectangle with length 5 cm and breadth 3 cm?

15 cm^2 Signup and view all the answers

What is the sum of the interior angles of a quadrilateral?

360° Signup and view all the answers

What is the name of the theorem that states the sum of the interior angles of a triangle is always 180°?

Angle Sum Property Signup and view all the answers

Which of the following is a type of quadrilateral where all sides are equal and opposite angles are equal?

Rhombus Signup and view all the answers

What is the term for a line that just touches a circle at one point?

Tangent Signup and view all the answers

What is the term for a quadrilateral inscribed in a circle?

Cyclic Quadrilateral Signup and view all the answers

What is the term for the process of solving geometric problems by applying properties and theorems to find unknown measurements?

Problem Solving Signup and view all the answers

What is the term for a transformation that involves flipping a shape over a line?

Reflection Signup and view all the answers

What is the term for a line that divides a shape into two identical halves?

Line of Symmetry Signup and view all the answers

What is the term for the process of using geometric tools to construct shapes accurately and measure their properties?

Construction and Measurement Signup and view all the answers

What is the key characteristic that defines similar shapes?

Same shape but not necessarily the same size Signup and view all the answers

What is the purpose of using scale factors in similar shapes?

To calculate the missing lengths of corresponding sides Signup and view all the answers

What is the main difference between a bar graph and a histogram?

The type of data being represented Signup and view all the answers

What is the purpose of analyzing the trend line in a scatter plot?

To determine the correlation between variables Signup and view all the answers

What is the key feature of a pie chart?

It shows the proportion of each segment to the whole Signup and view all the answers

What is the purpose of using the property of corresponding angles in similar shapes?

To apply the property that corresponding angles of similar shapes are equal Signup and view all the answers

What is the main difference between a line graph and a scatter plot?

The type of data being represented Signup and view all the answers

What is the purpose of interpreting the axis labels in a graph?

To understand what each axis represents Signup and view all the answers

What is the key feature of a composite figure?

It breaks down complex figures into simpler components Signup and view all the answers

What is the purpose of using logical reasoning and geometric principles in geometric proofs?

To support conclusions and establish relationships between different parts of geometric figures Signup and view all the answers

Math Gr 9 Nov Exam (Medium)

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Questions and Answers

What is the commutative property of addition?

Which of the following properties is not applicable to subtraction and division?

What is the associative property of multiplication?

What is the additive property of 0?

What is the purpose of using the distributive property of multiplication over addition?

How can the commutative and associative properties help in simplifying calculations?

What is the purpose of estimating in calculations with whole numbers?

What is the purpose of a summary table for multiplication?

What is the definition of a multiple of a number?

What is the definition of a prime number?

What is the purpose of finding the least common multiple (LCM)?

What is the process of expressing a number as the product of its prime factors?

What is the definition of a composite number?

What is the formula for calculating distance?

What is the purpose of finding the highest common factor (HCF)?

How do you find the time required to process a certain amount based on a rate?

What is the definition of a rate?

What is the purpose of expressing a ratio?

What is the result of adding a positive integer to its additive inverse?

What is the effect of subtracting a positive integer from a number?

What is the product of a positive integer and a negative integer?

What property of integers allows flexibility in computation and simplification?

What is the purpose of rounding off numbers in calculations?

What is the result of adding a negative integer to a number?

What is the method of breaking down numbers into parts and adding each part separately?

What is the symbol used to indicate 'greater than' in comparing integers?

What is the result of multiplying a positive integer and a positive integer?

What is the technique of rearranging parts to make subtraction easier by borrowing from higher place values?

What is the method of multiplying numbers by breaking down the multiplication into smaller parts and summing the partial products?

What is the result of dividing a positive integer by a negative integer?

What is the purpose of compensating in calculations?

What is the purpose of the Distributive Property of integers?

What is the result of subtracting a negative integer from a number?

What is the method of aligning numbers vertically by their place values and adding each column?

What is the method of dividing a number step-by-step, starting with the leftmost digits of the dividend?

What is the term for the leftover value when dividing a number?

What is the method of subtracting numbers by aligning them by their place values and subtracting each column?

What is the purpose of carrying over in multiplication?

What is the property of addition that states that changing the order of the numbers does not change the sum?

What is the property of multiplication that states that changing the grouping of the numbers does not change the product?

What is the formula to calculate simple interest?

What is the property of multiplication that states that multiplication distributes over addition?

What is the result of subtracting a positive integer from another positive integer?

What is the additive inverse of an integer?

What is the result of adding two positive integers?

What is the process of dividing quantities in a ratio?

What is the marked price of an article if the selling price is $120 and the discount is 20%?

What is the result of subtracting a larger integer from a smaller one?

What is the result of multiplying two integers with the same sign?

What is the absolute value of -5?

What is the result of multiplying a positive integer and a negative integer?

What is the formula for equivalent fractions?

What is the formula to calculate profit percentage?

What is the purpose of finding equivalent fractions?

What is the result of adding a positive integer and a negative integer?

What is the result of multiplying a fraction by a non-zero number?

What is the cube of -2?

What is the process of scaling quantities in a recipe?

What is the first step in multiplying decimal fractions?

When dividing a total amount by a certain number of people, what is the first step?

What is the purpose of the additive inverse in integer operations?

What is the result of adding an integer and its additive inverse?

What is the purpose of the commutative property of multiplication?

What is the result of subtracting an integer from itself?

What is the purpose of converting the divisor to a whole number in division of decimal fractions?

What is the result of adding an integer and its negative counterpart?

What is the purpose of adjusting the decimal point in the result of multiplication of decimal fractions?

What is the purpose of using the associative property of addition in decimal operations?

What property of integers allows for flexibility in computation and simplification?

What is the result of raising a number to the power of zero?

What is the first step in adding or subtracting fractions?

What is the product of a negative integer and a negative integer?

How do you multiply fractions?

What is the purpose of expressing large numbers in scientific notation?

What is the reciprocal of a fraction?

What is the result of cubing a fraction?

How do you simplify a fraction?